Image reconstruction for compressed sensing based on joint sparse bases and adaptive sampling

In this paper, we focus on tackling the problem that one sparse base alone cannot represent the different content of the image well in the image reconstruction for compressed sensing, and the same sampling rate is difficult to ensure the precise reconstruction for the different content of the image. To address this challenge, this paper proposed a novel approach that utilized two sparse bases for the representation of image. Moreover, in order to achieve better reconstruction result, the adaptive sampling has been used in the sampling process. Firstly, DCT and a double-density dual-tree complex wavelet transform were utilized as two different sparse bases to represent the image alternatively in a smoothed projected Landweber reconstruction algorithm. Secondly, different sampling rates were adopted for the reconstruction of different image blocks after segmenting the entire image. Experimental results demonstrated that the images reconstructed with the two bases were largely superior to that reconstructed with a single base, and the PSNR could be improved further after using the adaptive sampling.